The probability that the project is completed within 33 weeks is to be determined. Concept Introduction: Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

Question

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Answer 1

Question

Chapter 18, Problem 14PA

(a)

Summary Introduction

Interpretation: The probability that the project is completed within 33 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(a)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 33 weeks deadline.

z=33−321.69=11.3=0.769

Refer probability distribution table.

For z≤0.769 .

P(z≤0.769)=0.77935 .

Hence, the probability that the project is completed within 33 weeks is 0.77935 .

(b)

Summary Introduction

Interpretation: The probability that the project is completed within 30 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(b)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 30 weeks deadline.

z=30−321.69=−21.3=−1.539

Refer probability distribution table.

For z≤−1.539 .

P(z≤−1.539)=0.06178 .

Hence, the probability that the project is completed within 30 weeks is 0.06178 .

(c)

Summary Introduction

Interpretation: The probability that the project is completed within 35 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(c)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 35 weeks deadline.

z=35−321.69=31.3=2.308

Refer probability distribution table.

For z≤2.308 .

P(z≤2.308)=0.99134 .

Hence, the probability that the project is completed within 35 weeks is 0.99134 .

(d)

Summary Introduction

Interpretation: The probability that the project is completed within 32 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(d)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 32 weeks deadline.

z=32−321.69=01.3=0

Refer probability distribution table.

There is no value for z=0 .

Hence, the probability that the project is completed within 32 weeks cannot be determined.

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Answer 2

Question

Chapter 18, Problem 14PA

(a)

Summary Introduction

Interpretation: The probability that the project is completed within 33 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(a)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 33 weeks deadline.

z=33−321.69=11.3=0.769

Refer probability distribution table.

For z≤0.769 .

P(z≤0.769)=0.77935 .

Hence, the probability that the project is completed within 33 weeks is 0.77935 .

(b)

Summary Introduction

Interpretation: The probability that the project is completed within 30 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(b)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 30 weeks deadline.

z=30−321.69=−21.3=−1.539

Refer probability distribution table.

For z≤−1.539 .

P(z≤−1.539)=0.06178 .

Hence, the probability that the project is completed within 30 weeks is 0.06178 .

(c)

Summary Introduction

Interpretation: The probability that the project is completed within 35 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(c)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 35 weeks deadline.

z=35−321.69=31.3=2.308

Refer probability distribution table.

For z≤2.308 .

P(z≤2.308)=0.99134 .

Hence, the probability that the project is completed within 35 weeks is 0.99134 .

(d)

Summary Introduction

Interpretation: The probability that the project is completed within 32 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(d)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 32 weeks deadline.

z=32−321.69=01.3=0

Refer probability distribution table.

There is no value for z=0 .

Hence, the probability that the project is completed within 32 weeks cannot be determined.

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Answer 3

Question

Chapter 18, Problem 14PA

(a)

Summary Introduction

Interpretation: The probability that the project is completed within 33 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(a)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 33 weeks deadline.

z=33−321.69=11.3=0.769

Refer probability distribution table.

For z≤0.769 .

P(z≤0.769)=0.77935 .

Hence, the probability that the project is completed within 33 weeks is 0.77935 .

(b)

Summary Introduction

Interpretation: The probability that the project is completed within 30 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(b)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 30 weeks deadline.

z=30−321.69=−21.3=−1.539

Refer probability distribution table.

For z≤−1.539 .

P(z≤−1.539)=0.06178 .

Hence, the probability that the project is completed within 30 weeks is 0.06178 .

(c)

Summary Introduction

Interpretation: The probability that the project is completed within 35 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(c)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 35 weeks deadline.

z=35−321.69=31.3=2.308

Refer probability distribution table.

For z≤2.308 .

P(z≤2.308)=0.99134 .

Hence, the probability that the project is completed within 35 weeks is 0.99134 .

(d)

Summary Introduction

Interpretation: The probability that the project is completed within 32 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(d)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 32 weeks deadline.

z=32−321.69=01.3=0

Refer probability distribution table.

There is no value for z=0 .

Hence, the probability that the project is completed within 32 weeks cannot be determined.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 18, Problem 14PA

(a)

Summary Introduction

Interpretation: The probability that the project is completed within 33 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(a)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 33 weeks deadline.

z=33−321.69=11.3=0.769

Refer probability distribution table.

For z≤0.769 .

P(z≤0.769)=0.77935 .

Hence, the probability that the project is completed within 33 weeks is 0.77935 .

(b)

Summary Introduction

Interpretation: The probability that the project is completed within 30 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(b)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 30 weeks deadline.

z=30−321.69=−21.3=−1.539

Refer probability distribution table.

For z≤−1.539 .

P(z≤−1.539)=0.06178 .

Hence, the probability that the project is completed within 30 weeks is 0.06178 .

(c)

Summary Introduction

Interpretation: The probability that the project is completed within 35 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(c)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 35 weeks deadline.

z=35−321.69=31.3=2.308

Refer probability distribution table.

For z≤2.308 .

P(z≤2.308)=0.99134 .

Hence, the probability that the project is completed within 35 weeks is 0.99134 .

(d)

Summary Introduction

Interpretation: The probability that the project is completed within 32 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(d)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 32 weeks deadline.

z=32−321.69=01.3=0

Refer probability distribution table.

There is no value for z=0 .

Hence, the probability that the project is completed within 32 weeks cannot be determined.

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Answer 5

Chapter 18, Problem 14PA

(a)

Summary Introduction

Interpretation: The probability that the project is completed within 33 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(a)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 33 weeks deadline.

z=33−321.69=11.3=0.769

Refer probability distribution table.

For z≤0.769 .

P(z≤0.769)=0.77935 .

Hence, the probability that the project is completed within 33 weeks is 0.77935 .

(b)

Summary Introduction

Interpretation: The probability that the project is completed within 30 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(b)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 30 weeks deadline.

z=30−321.69=−21.3=−1.539

Refer probability distribution table.

For z≤−1.539 .

P(z≤−1.539)=0.06178 .

Hence, the probability that the project is completed within 30 weeks is 0.06178 .

(c)

Summary Introduction

Interpretation: The probability that the project is completed within 35 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(c)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 35 weeks deadline.

z=35−321.69=31.3=2.308

Refer probability distribution table.

For z≤2.308 .

P(z≤2.308)=0.99134 .

Hence, the probability that the project is completed within 35 weeks is 0.99134 .

(d)

Summary Introduction

Interpretation: The probability that the project is completed within 32 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(d)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 32 weeks deadline.

z=32−321.69=01.3=0

Refer probability distribution table.

There is no value for z=0 .

Hence, the probability that the project is completed within 32 weeks cannot be determined.

Answer 6

Chapter 18, Problem 14PA

(a)

Summary Introduction

Interpretation: The probability that the project is completed within 33 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(a)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 33 weeks deadline.

z=33−321.69=11.3=0.769

Refer probability distribution table.

For z≤0.769 .

P(z≤0.769)=0.77935 .

Hence, the probability that the project is completed within 33 weeks is 0.77935 .

Answer 7

Chapter 18, Problem 14PA

(a)

Summary Introduction

Interpretation: The probability that the project is completed within 33 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

Answer 8

(a)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 33 weeks deadline.

z=33−321.69=11.3=0.769

Refer probability distribution table.

For z≤0.769 .

P(z≤0.769)=0.77935 .

Hence, the probability that the project is completed within 33 weeks is 0.77935 .

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

(b)

Summary Introduction

Interpretation: The probability that the project is completed within 30 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(b)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 30 weeks deadline.

z=30−321.69=−21.3=−1.539

Refer probability distribution table.

For z≤−1.539 .

P(z≤−1.539)=0.06178 .

Hence, the probability that the project is completed within 30 weeks is 0.06178 .

Answer 13

(b)

Summary Introduction

Interpretation: The probability that the project is completed within 30 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

Answer 14

(b)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 30 weeks deadline.

z=30−321.69=−21.3=−1.539

Refer probability distribution table.

For z≤−1.539 .

P(z≤−1.539)=0.06178 .

Hence, the probability that the project is completed within 30 weeks is 0.06178 .

Answer 15

(b)

Expert Solution

Answer 16

(b)

Expert Solution

Answer 17

Expert Solution

Answer 18

(c)

Summary Introduction

Interpretation: The probability that the project is completed within 35 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(c)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 35 weeks deadline.

z=35−321.69=31.3=2.308

Refer probability distribution table.

For z≤2.308 .

P(z≤2.308)=0.99134 .

Hence, the probability that the project is completed within 35 weeks is 0.99134 .

Answer 19

(c)

Summary Introduction

Interpretation: The probability that the project is completed within 35 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

Answer 20

(c)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 35 weeks deadline.

z=35−321.69=31.3=2.308

Refer probability distribution table.

For z≤2.308 .

P(z≤2.308)=0.99134 .

Hence, the probability that the project is completed within 35 weeks is 0.99134 .

Answer 21

(c)

Expert Solution

Answer 22

(c)

Expert Solution

Answer 23

Expert Solution

Answer 24

(d)

Summary Introduction

Interpretation: The probability that the project is completed within 32 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(d)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444

Table (2)

Calculate z value to find the probability of meeting a 32 weeks deadline.

z=32−321.69=01.3=0

Refer probability distribution table.

There is no value for z=0 .

Hence, the probability that the project is completed within 32 weeks cannot be determined.

Answer 25

(d)

Summary Introduction

Interpretation: The probability that the project is completed within 32 weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

Answer 26

(d)

Expert Solution

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time
A	4	5	6
B	2.5	3	3.5
C	6	7	8
D	5	5.5	9
E	6	7	8
F	1	3	5
G	8	10	12

Table (1)

The expression for the estimated time is given by,

te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

Variance=(tp−t0)236

The variance and estimated time of each activity is tabulated below.

Activity	Optimistic time	Most Probable Time	Pessimistic Time	Estimated Time	Variance
A	4	5	6	5	0.111
B	2.5	3	3.5	3	0.028
C	6	7	8	7	0.111
D	5	5.5	9	6	0.444
E	6	7	8	7	0.111
F	1	3	5	3	0.444
G	8	10	12	10	0.444